Align vertex with edge or rather the imagine line between two verticies
Your goal is not fully specified by the imaginary line.. the sharp edges could be flattened to any plane that contains it.. (they could be twisted at any angle around the line)

If there is a plane you want to flatten to:


In the Pivot Center menu in the header, select 'Active Element'
Select three vertices which define the plane (possibly including the ones at the ends of your imaginary line)
Hit Ctrl Alt Space to create a Custom Orientation from them, checking 'Use after Creation'
Select the edges you want to flatten, and then, in vertex mode, one of the vertices that defined the plane
Hit  S Z Z 0 to scale the edges onto the plane.